A259654
a(n) = prime(n)^prime(n) - prime(n)^n.
Original entry on oeis.org
2, 18, 3000, 821142, 285311509560, 302875101765444, 827240261885926425504, 1978419655660296605560938, 20880467999847912032553880249104, 2567686153161211134561828214310308893183268, 17069174130723235958610643029033906279148329600
Offset: 1
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[NthPrime(n)^NthPrime(n)-NthPrime(n)^n: n in [1..12]]; // Vincenzo Librandi, Jul 03 2015
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Table[Prime[n]^Prime[n] - Prime[n]^n, {n, 1, 10}]
#[[1]]^#[[1]]-#[[1]]^#[[2]]&/@Table[{Prime[n],n},{n,15}] (* Harvey P. Dale, Nov 10 2016 *)
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a(n,p=prime(n))=p^p - p^n \\ Charles R Greathouse IV, Jul 22 2016
A259923
a(n) = prime(n)^pi(n).
Original entry on oeis.org
1, 3, 25, 49, 1331, 2197, 83521, 130321, 279841, 707281, 28629151, 69343957, 4750104241, 6321363049, 10779215329, 22164361129, 2488651484819, 3142742836021, 406067677556641, 645753531245761, 806460091894081, 1517108809906561, 186940255267540403, 350356403707485209, 760231058654565217
Offset: 1
For n = 1, a(1) = 2^0 = 1.
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[NthPrime(n)^#PrimesUpTo(n): n in [1..30]]; // Vincenzo Librandi, Aug 03 2015
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Table[Prime[n]^PrimePi[n], {n, 1, 25}]
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vector(30, n, prime(n)^primepi(n)) \\ Michel Marcus, Jul 09 2015
A276650
Primes of the form prime(k)^k - PrimePi(k).
Original entry on oeis.org
2, 2399, 1801152661459, 73885357344138503765443
Offset: 1
2 is in the sequence because 2 is prime and 2 = prime(1)^1 - PrimePi(1) = 2^1 - 0.
2399 is in the sequence because 2399 is prime and 2399 = prime(4)^4 - PrimePi(4) = 7^4 - 2.
1801152661459 is in the sequence because 1801152661459 is prime and 1801152661459 = prime(9)^9 - PrimePi(9) = 23^9 - 4.
73885357344138503765443 is in the sequence because 73885357344138503765443 is prime and 73885357344138503765443 = prime(14)^14 - PrimePi(14) = 43^14 - 6.
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Select[Map[Prime[#]^# - PrimePi@ # &, Range@ 1500], PrimeQ] (* Michael De Vlieger, Sep 26 2016 *)
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max_n = 20
seq = []
for n in range(1, max_n+1):
p = nth_prime(n)^n - prime_pi(n)
if is_prime(p):
seq.append(p)
print(seq)
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